View example sentences, synonyms and word forms for Idempotent.
Idempotent meaning
(said of a function) Such that, when performed multiple times on the same subject, it has no further effect on its subject after the first time it is performed. | (said of an element of an algebraic structure with a binary operation, such as a group or semigroup) Such that, when it operates on itself, the result is equal to itself. | (said of a binary operation) Such that all of the distinct elements it can operate on are idempotent (in the sense given just above).
Synonyms of Idempotent
Example sentences (20)
An idempotent semiring (also sometimes called a dioid) is a semiring whose addition (not multiplication) is idempotent.
The binary operation itself is called idempotent if every element of is idempotent.
While "idempotent" usually refers to the multiplication operation of a ring, there are rings in which both operations are idempotent: Boolean algebras are such an example.
As in the example above, reading data usually has no side effects, so it is idempotent (in fact nullipotent).
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic.
Canceling an order is idempotent, because the order remains canceled no matter how many requests are made.
Commutative idempotent quasigroups satisfying this additional property are called Steiner quasigroups.
Each step in the sequence is idempotent: both steps reading the variable have no side effects and changing a variable to 5 will always have the same effect no matter how many times it is executed.
Examples A function looking up a customer's name and address in a database is typically idempotent, since this will not cause the database to change.
Finally, an inverse semigroup with only one idempotent is a group.
For each idempotent e of the semigroup there is a unique maximal subgroup containing e. Each maximal subgroup arises in this way, so there is a one-to-one correspondence between idempotents and maximal subgroups.
For example, every nonempty finite semigroup is periodic, and has a minimal ideal and at least one idempotent.
Formal languages The Kleene star and Kleene plus operators used to express repetition in formal languages are idempotent.
However, placing an order for a car for the customer is typically not idempotent, since running the call several times will lead to several orders being placed.
If a method is unknown to an intermediate it will be treated as an unsafe and non-idempotent method.
In contrast, the POST method is not necessarily idempotent, and therefore sending an identical POST request multiple times may further affect state or cause further side effects (such as financial transactions ).
In each case, subsequent executions will further modify the state of the system, so they are not idempotent.
In On a conjecture of Littlewood and idempotent measures (1960) Cohen made a significant breakthrough in solving the Littlewood Conjecture. citation.
It follows that every nonempty periodic semigroup has at least one idempotent.
It is an example of a closure operator ; all closure operators are idempotent functions.